Finite Group Databasebeta

← #24992574

Subgroups — #24992574

Order 11008.

580 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 580 conjugacy classes of subgroups — too many to draw. Only its 91 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19143634C211yesmaximal, characteristic, complemented
2#19140482C211yesmaximal, characteristic
3C4×#13063239C211yesmaximal, characteristic, complemented
4#19133112C211yesmaximal, characteristic, complemented
5#19133110C211yesmaximal, characteristic, complemented
6#19132447C211yesmaximal, characteristic, complemented
7C43×#1284C211yesmaximal, characteristic, complemented
8C2×#13063299C2211yescharacteristic
9C2×C4×C22⋊D43C2211yescharacteristic
10#14582975—22no—
11#14582974—22no—
12#14582949—21no—
13C2×#13063239—21no—
14#14582863C2211yescharacteristic
15#14582861—21no—
16#14582839C411yescharacteristic, complemented
17#14582836C411yescharacteristic, complemented
18#14582817C411yescharacteristic, complemented
19#14582815—21no—
20#14582809C411yescharacteristic, complemented
21#14582808—21no—
22#14582791—21no—
23#14582777—21no—
24C4×C22⋊Dic43C2211yescharacteristic
25#14582665—21no—
26#14582634—22no—
27#14582632—22no—
28C43×#407C2211yescharacteristic
29C43×#381C2211yescharacteristic
30C4×C22⋊C4×C43C2211yescharacteristic
31C22×D172—21no—
32C22×D172C2×C411yescharacteristic
33C22×C22⋊D43—21no—
34C22×C22⋊D43D411yescharacteristic
35C22×C4×D43D411yescharacteristic
36C2×#10621877—21no—
37C2×#10621872—22no—
38#13063299—21no—
39#13063299—21no—
40#13063299—21no—
41#13063299—21no—
42C4×C22⋊D43—21no—
43C4×C22⋊D43—21no—
44C4×C22⋊D43—21no—
45C4×C22⋊D43—21no—
46C2×C4⋊Dic43—21no—
47C2×C4⋊Dic43C2×C411yescharacteristic
48C2×Dic43⋊C4C2×C411yescharacteristic
49C2×C22⋊Dic43—21no—
50C2×C22⋊Dic43D411yescharacteristic
51C2×(C2×D43)⋊C4—21no—
52C2×(C2×D43)⋊C4—21no—
53C2×(C2×D43)⋊C4—21no—
54C2×(C2×D43)⋊C4—21no—
55C2×(C2×D43)⋊C4—21no—
56C2×(C2×D43)⋊C4C2×C411yescharacteristic
57C2×C4×Dic43—21no—
58C2×C4×Dic43D411yescharacteristic
59Dic43⋊C8—22no—
60#13063239—24no—
61C22⋊(C43⋊C8)—21no—
62C22⋊(C43⋊C8)D412yescomplemented
63(C2×D43)⋊C8—22no—
64C8×Dic43—22no—
65C43⋊#95—21no—
66C43⋊#95—21no—
67C43⋊#95—21no—
68C23×C4×C43C2311yescharacteristic
69C2×M16×C43—21no—
70C2×C22⋊C4×C43—21no—
71C2×C22⋊C4×C43—21no—
72C2×C42×C43—21no—
73C22⋊C8×C43—21no—
74C22⋊C8×C43D412yescomplemented
75#95×C43—21no—
76#95×C43—21no—
77#95×C43C2×C411yescharacteristic
78#95×C43C2×C411yescharacteristic
79C24×C43C2×D411yescharacteristic
80C23×D43—21no—
81C23×D43C22⋊C411yescharacteristic
82C22×C4×C43—21no—
83C22×C4×C43—21no—
84C22×C4×C43—41no—
85C22×C4×C43—81no—
86C22×C4×C43C22×C411yescharacteristic
87C22×C4×C43C2×D411yescharacteristic
88C22×C4×C43C2×D411yescharacteristic
89C22×C4×C43C2×D411yescharacteristic
90C22×C4×C43#4111yescharacteristic
91C22×C4×C43#4111yescharacteristic
92C2×C22⋊D43—22no—
93C2×C22⋊D43—21no—
94C2×C22⋊D43—21no—
95C2×C22⋊D43—41no—
96C2×C22⋊D43—41no—
97C2×C22⋊D43—41no—
98C2×C22⋊D43—81no—
99C2×C22⋊D43—81no—
100C22×Dic43—21no—
101C22×Dic43—41no—
102C22×Dic43C22⋊C411yescharacteristic
103C22×Dic43C22⋊C411yescharacteristic
104C22×Dic43C22⋊C411yescharacteristic
105C2×D172—21no—
106C2×D172—21no—
107C2×D172—42no—
108C2×D172—81no—
109C2×D172—81no—
110C2×D172—81no—
111C2×C4×D43—21no—
112C2×C4×D43—21no—
113C2×C4×D43—81no—
114M16×C43—81no—
115C2×C8×C43—22no—
116C22⋊C4×C43—22no—
117C22⋊C4×C43—41no—
118C22⋊C4×C43—81no—
119C42×C43—81no—
120C22⋊Dic43—22no—
121C22⋊Dic43—21no—
122C22⋊Dic43—21no—
123C22⋊Dic43—41no—
124(C2×D43)⋊C4—21no—
125(C2×D43)⋊C4—21no—
126(C2×D43)⋊C4—41no—
127(C2×D43)⋊C4—41no—
128(C2×D43)⋊C4—42no—
129(C2×D43)⋊C4—81no—
130(C2×D43)⋊C4—81no—
131(C2×D43)⋊C4—81no—
132C4⋊Dic43—21no—
133C4⋊Dic43—21no—
134C4⋊Dic43—81no—
135Dic43⋊C4—21no—
136Dic43⋊C4—21no—
137C4×Dic43—21no—
138C4×Dic43—21no—
139C4×Dic43—81no—
140#10621877—81no—
141C2×C43⋊C8—22no—
142#10621872—82no—
143C23×C43—21no—
144C23×C43—21no—
145C23×C43—41no—
146C23×C43—41no—
147C23×C43C2×C22⋊C411yescharacteristic
148C23×C43#12111yescharacteristic
149C23×C43#12111yescharacteristic
150C22×D43—21no—
151C22×D43—21no—
152C22×D43—21no—
153C22×D43—41no—
154C22×D43—41no—
155C22×D43—41no—
156C22×D43—41no—
157C22×D43—41no—
158C22×D43—41no—
159C22×D43—41no—
160C22×D43—41no—
161C22×D43—41no—
162C2×C4×C43—41no—
163C2×C4×C43—41no—
164C2×C4×C43—41no—
165C2×C4×C43—41no—
166C2×C4×C43—41no—
167C2×C4×C43—41no—
168C2×C4×C43—41no—
169C2×C4×C43—41no—
170C2×C4×C43—41no—
171C2×C4×C43—42no—
172C2×C4×C43—41no—
173C2×C4×C43—41no—
174C2×C4×C43—41no—
175C2×C4×C43—81no—
176C2×C4×C43—81no—
177C2×C4×C43C4×D411yescharacteristic
178C2×C4×C43C4×D411yescharacteristic
179C2×C4×C43#12011yescharacteristic
180C2×C4×C43#12311yescharacteristic
181C22⋊D43—42no—
182C22⋊D43—42no—
183C22⋊D43—82no—
184C22⋊D43—82no—
185C2×Dic43—21no—
186C2×Dic43—21no—
187C2×Dic43—21no—
188C2×Dic43—21no—
189C2×Dic43—41no—
190C2×Dic43—41no—
191C2×Dic43—41no—
192C2×Dic43—41no—
193C2×Dic43—42no—
194C2×Dic43—41no—
195C2×Dic43—81no—
196C2×Dic43—81no—
197C2×Dic43#10412yes—
198D172—81no—
199D172—81no—
200D172—84no—
201C4×D43—42no—
202C4×D43—81no—
203C8×C43—42no—
204C43⋊C8—42no—
205#9186—431nomaximal, Sylow
206C22×C43—21no—
207C22×C43—21no—
208C22×C43—21no—
209C22×C43—21no—
210C22×C43—21no—
211C22×C43—21no—
212C22×C43—21no—
213C22×C43—21no—
214C22×C43—81no—
215C22×C43—81no—
216C22×C43#38611yescharacteristic
217C22×C43C2×#10411yescharacteristic
218C22×C43#42111yescharacteristic
219C2×D43—42no—
220C2×D43—41no—
221C2×D43—41no—
222C2×D43—41no—
223C2×D43—81no—
224C2×D43—81no—
225C2×D43—81no—
226C2×D43—81no—
227C2×D43—81no—
228C2×D43—81no—
229C2×D43—81no—
230C2×D43—81no—
231C4×C43—21no—
232C4×C43—21no—
233C4×C43—21no—
234C4×C43—21no—
235C4×C43—81no—
236C4×C43—81no—
237C4×C43—82no—
238Dic43—22no—
239Dic43—41no—
240Dic43—41no—
241Dic43—82no—
242Dic43—81no—
243#2975—431no—
244#2635—431no—
245C4×#99—431no—
246#1507—431no—
247#1507—431no—
248#1284—431no—
249#1284D4311yescharacteristic, complemented
250C2×C43—21no—
251C2×C43—21no—
252C2×C43—41no—
253C2×C43—41no—
254C2×C43#187111yescharacteristic
255C2×C43#191011yescharacteristic
256C2×C43#191311yescharacteristic
257D43—81no—
258D43—161no—
259C2×#121—431no—
260C2×C4×D4—431no—
261#436—862no—
262#436—862no—
263#431—861no—
264C2×#99—861no—
265#407—431no—
266#407—861no—
267#407C2×D4311yescharacteristic
268#400—431no—
269#399—431no—
270#394—431no—
271#394—861no—
272#392—431no—
273#392—861no—
274#388—861no—
275#386—861no—
276#381C2×D4311yescharacteristic
277C4×C22⋊C4—431no—
278C4×C22⋊C4C2×D4311yescharacteristic
279#342—861no—
280#327—862no—
281#327—862no—
282C43#918611yescharacteristic, complemented, Sylow
283C22×D4—431no—
284C22×D4—431no—
285C22×D4—861no—
286C22×D4—861no—
287C23×C4—431no—
288C23×C4C22×D4311yescharacteristic
289C2×M16—21no—
290C2×M16—862no—
291C2×M16—861no—
292#121—861no—
293#121—861no—
294#121—861no—
295#121—861no—
296C4×D4—861no—
297C4×D4—861no—
298C4×D4—861no—
299C4×D4—861no—
300C2×C4⋊C4—431no—
301C2×C4⋊C4—431no—
302C2×C4⋊C4—861no—
303C2×C22⋊C4—21no—
304C2×C22⋊C4—21no—
305C2×C22⋊C4—431no—
306C2×C22⋊C4—431no—
307C2×C22⋊C4—861no—
308C2×C22⋊C4—861no—
309C2×C22⋊C4—861no—
310C2×C22⋊C4—861no—
311C2×C22⋊C4—861no—
312C2×C22⋊C4—861no—
313C2×C42—21no—
314C2×C42—431no—
315C2×C42—861no—
316C4⋊C8—862no—
317#99—864no—
318C22⋊C8—21no—
319C22⋊C8—432no—
320C22⋊C8—862no—
321C22⋊C8—861no—
322C22⋊C8D17212yescomplemented
323C4×C8—862no—
324#95—21no—
325#95—21no—
326#95—861no—
327#95—861no—
328#95—861no—
329#95C4×D4311yescharacteristic
330#95C4×D4311yescharacteristic
331C24—431no—
332C24—861no—
333C24D4×D4311yescharacteristic
334C2×D4—862no—
335C2×D4—861no—
336C2×D4—861no—
337C2×D4—861no—
338C2×D4—861no—
339C2×D4—3441no—
340C2×D4—3441no—
341C2×D4—3441no—
342C2×D4—3441no—
343C2×D4—3441no—
344C2×D4—1722no—
345C2×D4—1721no—
346C2×D4—1721no—
347C2×D4—1721no—
348C22×C4—21no—
349C22×C4—21no—
350C22×C4—41no—
351C22×C4—81no—
352C22×C4—431no—
353C22×C4—431no—
354C22×C4—431no—
355C22×C4—861no—
356C22×C4—861no—
357C22×C4—861no—
358C22×C4—3441no—
359C22×C4—1721no—
360C22×C4C2×C4×D4311yescharacteristic
361C22×C4C2×D17211yescharacteristic
362C22×C4#1062189811yescharacteristic
363C22×C4D4×D4311yescharacteristic
364C22×C4D4×D4311yescharacteristic
365C22×C4#1062190211yescharacteristic
366M16—81no—
367M16—3442no—
368M16—3441no—
369C2×C8—22no—
370C2×C8—862no—
371C4⋊C4—861no—
372C4⋊C4—861no—
373C4⋊C4—861no—
374C4⋊C4—861no—
375C4⋊C4—3441no—
376C22⋊C4—22no—
377C22⋊C4—41no—
378C22⋊C4—81no—
379C22⋊C4—861no—
380C22⋊C4—861no—
381C22⋊C4—861no—
382C22⋊C4—861no—
383C22⋊C4—862no—
384C22⋊C4—3441no—
385C22⋊C4—3441no—
386C22⋊C4—3441no—
387C22⋊C4—1722no—
388C22⋊C4—1721no—
389C22⋊C4—1721no—
390C22⋊C4—1721no—
391C42—81no—
392C42—861no—
393C42—861no—
394C42—3441no—
395C23—21no—
396C23—21no—
397C23—41no—
398C23—41no—
399C23—861no—
400C23—861no—
401C23—861no—
402C23—1721no—
403C23—1721no—
404C23—1721no—
405C23—1721no—
406C23—1721no—
407C23—1721no—
408C23—1721no—
409C23—1721no—
410C23—1721no—
411C23C22⋊C4×D4311yescharacteristic
412C23#1306329811yescharacteristic
413C23#1306330011yescharacteristic
414D4—3441no—
415D4—3441no—
416D4—3444no—
417D4—3442no—
418D4—3442no—
419D4—1722no—
420D4—1722no—
421C2×C4—41no—
422C2×C4—41no—
423C2×C4—41no—
424C2×C4—41no—
425C2×C4—41no—
426C2×C4—41no—
427C2×C4—42no—
428C2×C4—41no—
429C2×C4—41no—
430C2×C4—41no—
431C2×C4—41no—
432C2×C4—41no—
433C2×C4—41no—
434C2×C4—81no—
435C2×C4—81no—
436C2×C4—432no—
437C2×C4—861no—
438C2×C4—861no—
439C2×C4—861no—
440C2×C4—861no—
441C2×C4—3441no—
442C2×C4—3441no—
443C2×C4—3441no—
444C2×C4—1722no—
445C2×C4—1722no—
446C2×C4—1721no—
447C2×C4—1721no—
448C2×C4—1721no—
449C2×C4—1721no—
450C2×C4—1721no—
451C2×C4#1306328711yescharacteristic
452C2×C4C4×D17211yescharacteristic
453C2×C4#1306329511yescharacteristic
454C2×C4#1306331011yescharacteristic
455C8—42no—
456C8—1722no—
457C22—21no—
458C22—21no—
459C22—21no—
460C22—21no—
461C22—21no—
462C22—21no—
463C22—21no—
464C22—21no—
465C22—81no—
466C22—81no—
467C22—3441no—
468C22—3441no—
469C22—3441no—
470C22—3441no—
471C22—3441no—
472C22—3441no—
473C22—3441no—
474C22—3441no—
475C22—1722no—
476C22—1721no—
477C22—1721no—
478C22—1721no—
479C22#1458277711yescharacteristic
480C22#104×D4311yescharacteristic
481C22#1458291411yescharacteristic
482C4—21no—
483C4—21no—
484C4—21no—
485C4—21no—
486C4—81no—
487C4—81no—
488C4—82no—
489C4—862no—
490C4—3442no—
491C4—3441no—
492C4—1721no—
493C4—1721no—
494C2—21no—
495C2—21no—
496C2—41no—
497C2—41no—
498C2—3441no—
499C2—6881no—
500C2#1913489611yescharacteristic
501C2#1913512111yescharacteristic
502C2#1913513611yescharacteristic
subgroupG/H
centerC22#14582777
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingC43×#1284C2
socleC22×C43#386
prime radical#19140482C2
cosocleC23×C4×C43C23
hypercenter#1284D43
hypocenterC43#9186
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1284

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #19143634C2semidirect
3. C4×#13063239C2semidirect
4. #19133112C2semidirect
5. #19133110C2semidirect
6. #19132447C2semidirect
7. C43×#1284C2semidirect
16. #14582839C4semidirect
17. #14582836C4semidirect
18. #14582817C4semidirect
20. #14582809C4semidirect
62. C22⋊(C43⋊C8)D4semidirect
74. C22⋊C8×C43D4semidirect
249. #1284D43semidirect
282. C43#9186semidirect
322. C22⋊C8D172semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#191436342
#191404822
C4×#130632392
#191331122
#191331102
#191324472
C43×#12842
#918643